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Calculus Algebra II Honors Advanced Algebra 1
Syllabus
Course: AP Calculus I
In this course, we will study two main concepts – the derivative and the integral. To ensure that a basic understanding of these principles is obtained we will begin with a thorough review of algebra and trigonometry and a development of the limit concept. Throughout the course, many practical applications of calculus will be presented and the student is expected to have a working knowledge of calculus in areas of science and business.
Text: Calculus by Larson, Hostetler, and Edwards, 8th Edition. D. C. Heath and Company, 2005.
Instructor: Mr. G Davidson
Outcomes: Students will know basic concepts and demonstrate calculus techniques in the following areas:
I Pre-Calculus Review – algebra and trigonometry and use of technology such as graphing calculators, graphical utilities, and spreadsheets (goal 6). We will make heavy use of graphing calculators to assist us in finding zeros, relative maximums and minimums, and other characteristics of functions.
2. Limits – develop the notions of closeness, continuity, function, and limit (goal 2). Limits at infinity and delta-epsilon proofs will also be studied.
3. Differentiation – students will learn the definition and how a function and its derivative are related graphically and algebraically. Differentiation rules will be applied to algebraic, trigonometric, logarithmic, exponential, and hyperbolic functions. Proper notation and development of rules will be emphasized (rules such as product, quotient, and chain and techniques such as implicit differentiation) (goal 3). We will utilize graphing calculators to assist us in approximating derivatives and in applications such as Newton’s method.
4. Application of Differentiation – students will apply what they learned in part 3 with most applications in the areas of graphing, business, and science (goal 1). Students will understand the dual concepts of rate of change and slope of the tangent line, how they are related, and how they are applied.
5. Integration – students will understand the concept of integration as an “antiderivative”, as an area, and its use in graphing (goal 4). Students will apply the Fundamental Theorem of Calculus and recognize when the 2nd Fundamental Theorem of Calculus can be applied. Students will also understand how the concept of Integration was derived and its culmination in the Riemann Integral.
6. Applications of Integration – students apply integration in finding area, volume, solutions to motion problems, and in graphing. The science concepts of work, fluid pressure and force will also be examined. We will utilize graphing calculators to approximate definite integrals using methods such as Simpson’s rule. (goal 4)
7. Exponential and Logarithmic Functions – students apply the derivative and integration to this class of functions. Also problems of growth and decay and how these are applied in science and business are studied.
- Trigonometric Functions – Students also apply the derivative and integration to trigonometry functions and their inverses and apply these functions to practical problems in science and in triangle and circle measurement.
- Differential Equations – Students learn a variety of techniques of solving differential equations and apply these techniques in problem solving. Also Euler’s method and slope fields in approximating solutions will be examined and we will utilize graphic calculators to assist us in making calculations and in examining the graphs of solutions.
- Students will be performing many problem solving activities which require responses verbally as well as written. In addition, most of my tests have open ended essay questions which require clear, concise, and complete responses. I expect students to know the language of calculus and to use it appropriately. (goals 1 and 5).
Policies: 1. Daily homework will be assigned.
2. Homework is due the day after it is assigned. Unexcused late homework will not be accepted. Occasionally there will be some class time for homework. Failure to use this time properly will result in a demerit.
3. A one hour test will follow each chapter.
4. A 15 minute quiz may be given at any time covering a specific topic.
5. A comprehensive semester exam will be given each semester.
6. Students will need a graphing calculator, preferably a TI-83 graphing calculator or better. Knowledge of MicroSoft Excel is helpful.
7. Any evidence of communicating during an exam will result in a zero for that exam.
8. All policies in the student handbook will be followed.
9. This course may be taken for 5 hours of Newman University credit and credit may also be obtained from other universities by taking the AP exam in May.
10. Extra help is available in room 402, before or after school. Since I administrate the school's PowerSchool program, I can occasionally be found in the network server room at those times (200 hall). Please have me paged in the main office if you have difficulty finding me. My email address is davidsongreg@bcchs.org. My voice mail phone number is 722-2390 extension 511.
11. A number of resources within the school will also be used. Students will make use of one of our computer labs in studying differentiation and integration. We will also apply technology in student numeric methods such as Newton’s method and the Trapezoidal rule. We will also view several videos on differentiation and integration. Usually, late in the fall, we have a former student visit us and give students an understanding of the use of calculus in college.
Grading: Grades will be computed using weighted averages. The weights of each area are given below.
Tests........................... 60%
Homework................... 20%
Quizzes........................ 10%
Final Test…………….. 10%
The Diocesan grading scale will be used.
Newman University grade will be the mean of the Bishop Carroll semester grades.
Syllabus
Course: Honors Algebra II
Test: Algebra and Trigonometry, Structure and Method, Book 2 by Brown, Dolciani, Sorgenfrey and Kane, McDougal Littell Publishing, 2000.
Instructor: Mr. G. Davidson
Outcomes: Students will demonstrate skill in problem solving in the following areas:
- Structures of Algebra – symbolic nature of algebra, variables, grouping symbols, operations, equations and the translation of English into these structures.
- Real number properties – Operations of real numbers and the distributive, commutative, and associative properties.
- Solving equations and word problems – Using transformations and inverses to solve equations.
- Polynomials – Definition of polynomial and operations with polynomials. Polynomials will be used in problem solving in science and measurement.
- Exponents and Logarithms – solving equations, simplifying expressions, and practical applications in growth and decay will be examined.
- Factoring Polynomials - The concept of factoring and the relationship between multiplication and division will be studied. Various techniques of factoring will be studied and their use in solving problems.
- Complex Numbers – Operations with complex numbers and algebraic expressions will be studied.
- Applications of Rational Expressions – Various topics will be explored using fractions, ratios, and proportions. These topics include mixtures, work, percents, and scientific notation.
- Functions – The concept of function will be studied with focus on linear and quadratic functions. Direct and Indirect variation will also be studied using the concept of function.
- Systems of Linear Equations – A variety of methods will be used to solve systems of linear equations. These will include graphing, substitution, an the addition method.
- Inequalities – Solving inequalities and systems of inequalities.
- Logarithms and exponential functions - .
- Quadratic Functions – Functions as well as equations will be studied. Various methods of solving quadratic equations will be explored.
- Matrices – Operations and applications of matrices will be studied.
- Analytic Geometry –The conic sections will be studied.
- Graphing – Students will be able to analyze and create graphs on paper as well as calculator.
Policies: 1. Daily homework will be assigned. Work should be done with pencil.
- Homework is due the day after it is assigned. Late homework will not be accepted. Occasionally there will be some class time for homework. Failure to use this time properly will result in a demerit.
- A one hour test will follow each chapter. These tests will cover outcomes for both Bishop Carroll Catholic High School and the State Math Assessment.
- A short quiz may be given at any time covering a specific topic. A comprehensive semester exam will be given each semester. It will cover the above outcomes and the emphasis will be on demonstrating basic skills in problem solving.
- It is recommended that students have a scientific calculator, preferably a TI-83, TI-84, or TI-86 graphing calculator. A knowledge of MicroSoft Excel is helpful, but not required. There will be some lab work and simulations performed on computers.
- Any evidence of communicating during an exam will result in a zero for that exam.
- All policies in the student handbook will be followed.
- No food or drink is allowed in the classroom unless prior approval is made.
- Extra help is available in room 402, before or after school. Since I help administrate the school’s computer network and PowerSchool, I can occasionally be found in the network server room or in the main office. Please have me paged in the office if you have difficulty finding me. My email address is davidsongreg@bcchs.org . My voice mail phone number is 722-2390 extension 511.
Grading: Grades will be computed using weighted averages. The weights of each area are given below.
Tests……………………………… 60%
Quizzes…………………………… 10%
Homework………………………… 20%
Semester Test……………………… 10%
The Diocesan grading scale will be used.
Syllabus
Course: Advanced Algebra I
Test: Algebra, Structure and Method, Book 1 by Brown, Dolciani, Sorgenfrey and Cole, McDougal Littell Publishing, 1997.
Instructor: Mr. G. Davidson
Outcomes: Students will demonstrate skill in problem solving in the following areas:
- Structures of Algebra – symbolic nature of algebra, variables, grouping symbols, operations, equations and the translation of English into these structures.
- Real number properties – Operations of real numbers and the distributive, commutative, and associative properties.
- Solving equations and word problems – Using transformations and inverses to solve equations.
- Polynomials – Definition of polynomial and operations with polynomials. Polynomials will be used in problem solving in science and measurement.
- Exponents and Logarithms – solving equations, simplifying expressions, and practical applications in growth and decay will be examined.
- Factoring Polynomials - The concept of factoring and the relationship between multiplication and division will be studied. Various techniques of factoring will be studied and their use in solving problems.
- Fractions – Operations with fractions with real numbers and algebraic expressions will be studied.
- Applications of Fractions – Various topics will be explored using fractions, ratios, and proportions. These topics include mixtures, work, percents, and scientific notation.
- Functions – The concept of function will be studied with focus on linear and quadratic functions. Direct and Indirect variation will also be studied using the concept of function.
- Systems of Linear Equations – A variety of methods will be used to solve systems of linear equations. These will include graphing, substitution, an the addition method.
- Inequalities – Solving inequalities and systems of inequalities.
- Rational and Irrational Numbers – Operations, properties, and variable expressions will be studied. In addition, the Pythagorean Theorem and simple radical equations will be examined.
- Quadratic Functions – Functions as well as equations will be studied. Various methods of solving quadratic equations will be explored.
- Finite Mathematics – Combinatorics, probability and statistics will be studied, independent of our textbook.
Policies: 1. Daily homework will be assigned.
- Homework is due the day after it is assigned. Late homework will not be accepted. Occasionally there will be some class time for homework. Failure to use this time properly will result in a demerit.
- A one hour test will follow each chapter. These tests will cover outcomes for both Bishop Carroll Catholic High School and the State Math Assessment.
- A short quiz may be given at any time covering a specific topic. A comprehensive semester exam will be given each semester. It will cover the above outcomes and the emphasis will be on demonstrating basic skills in problem solving.
- It is recommended that students have a scientific calculator, preferably a TI-83 or TI-86 graphing calculator. A knowledge of MicroSoft Excel is helpful, but not required. There will be some lab work and simulations performed on computers.
- Any evidence of communicating during an exam will result in a zero for that exam.
- All policies in the student handbook will be followed.
- Extra help is available in room 402, before or after school. Since I help administrate the school’s computer network and PowerSchool, I can occasionally be found in the network server room or in the main office. Please have me paged in the office if you have difficulty finding me. My email address is davidsongreg@bcchs.org . My voice mail phone number is 722-2390 extension 511.
Grading: Grades will be computed using weighted averages. The weights of each area are given below.
Tests……………………………… 60%
Quizzes…………………………… 10%
Homework………………………… 20%
Semester Test……………………… 10%
The Diocesan grading scale will be used.
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